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3 Answers
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No, his creatures will not have summoning sickness. He will control them continuously since the beginning of his turn.

302.6. A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control continuously since his or her most recent turn began. A creature can't attack unless it has been under its controller's control continuously since his or her most recent turn began. This rule is informally called the "summoning sickness" rule.

His creatures will not have summoning sickness and can attack normally.

The rule informally known as summoning sickness says that a creature permanent cannot attack or use abilities with the tap or untap symbol in their costs if its controller did not control it from the beginning of his last turn.

However, that rule does not apply here, since your opponent got his permanents back during your turn, even if it's at the end of your turn. He will start his turn with all permanents in play, so summoning sickness is not an issue for them.

And in particular, only abilities that actually use the tap symbol in their cost.
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David ZSep 3 '12 at 18:25

Yes, only attacking, the tap symbol and the untap symbol look for summoning sickness. Arachnus Spinner doesn't use the tap symbol, so it could tap itself the turn is was cast!
–
ikegamiSep 4 '12 at 18:10